An important question which discrete approaches to quantum gravity must
address is how continuum features of spacetime can be recovered from the
discrete substructure. We examine this question in the causal set
approach to quantum gravity. By defining a new topology on causal sets,
we show that it is possible to recover the homology of the continuum from
a causal set which embeds into a globally hyperbolic spacetime at
sufficiently high sprinkling density.